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Research questionHow can residual networks approximate high-dimensional semilinear heat-equation solutions without exponential parameter growth?High-dimensional PDE solvers can require resources that grow exponentially with dimension. It is therefore unclear whether residual architectures can represent solutions to nonlinear PDEs with only polynomial parameter growth.
AI
Machine Learning
Neural and Evolutionary Computing
Research Paper
Latest papersRecent research connected to this question, newest first.Residual neural networks overcome the curse of dimensionality for semilinear heat equationsThe result applies under polynomial-growth and network-approximability assumptions on the PDE data, with globally Lipschitz, gradient-independent nonlinearities. For ridge-sum initial conditions, admissible sigmoidal activations, and globally Lipschitz truncations, it gives an explicit parameter bound of Cξ d^(4+ξ) ε^-(3+ξ); the evidence is theoretical and establishes existence of suitable ResNets.research paper · Sep 3, 2026
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